Doubt from PNC

Suppose i have 5a and 6b i want to form word so that the word is a pallendrome(a word which reads same from front and backwards like noon,nitin,etc) how many ways it will be?

Yes please tell how did you do,it was a challenging question given by our sir

In total there are 11 letters.. So the middle letter has to be 'a'. Both sides of a contain 2 a's and 3b's each... If we arrange one side, the other side is automatically done for it is just a mirror image of the previous arrangement...So on one side of a there are five vacant placed out of which three have to be chosen for b's.. This can be done in 5C3 ways.. The others can be arranged in exactly one way.. Hence, the required answer is 5C3=10..

Does the palindrome have to be of 11 letters?